Abstract:The practice of fine-tuning Large Language Models (LLMs) has achieved state-of-the-art performance on specialized tasks, yet diagnosing why these models become brittle and fail to generalize remains a critical open problem. To address this, we introduce and apply a multi-layered diagnostic framework to a cross-architectural study. We fine-tune Llama 3.1 8B, Gemma 2 9B, and Mistral models on a high-stakes phishing detection task and use SHAP analysis and mechanistic interpretability to uncover the root causes of their generalization failures. Our investigation reveals three critical findings: (1) Generalization is driven by a powerful synergy between architecture and data diversity. The Gemma 2 9B model achieves state-of-the-art performance (>91\% F1), but only when trained on a stylistically diverse ``generalist'' dataset. (2) Generalization is highly architecture-dependent. We diagnose a specific failure mode in Llama 3.1 8B, which performs well on a narrow domain but cannot integrate diverse data, leading to a significant performance drop. (3) Some architectures are inherently more generalizable. The Mistral model proves to be a consistent and resilient performer across multiple training paradigms. By pinpointing the flawed heuristics responsible for these failures, our work provides a concrete methodology for diagnosing and understanding generalization failures, underscoring that reliable AI requires deep validation of the interplay between architecture, data, and training strategy.




Abstract:Elastic Riemannian metrics have been used successfully in the past for statistical treatments of functional and curve shape data. However, this usage has suffered from an important restriction: the function boundaries are assumed fixed and matched. Functional data exhibiting unmatched boundaries typically arise from dynamical systems with variable evolution rates such as COVID-19 infection rate curves associated with different geographical regions. In this case, it is more natural to model such data with sliding boundaries and use partial matching, i.e., only a part of a function is matched to another function. Here, we develop a comprehensive Riemannian framework that allows for partial matching, comparing, and clustering of functions under both phase variability and uncertain boundaries. We extend past work by: (1) Forming a joint action of the time-warping and time-scaling groups; (2) Introducing a metric that is invariant to this joint action, allowing for a gradient-based approach to elastic partial matching; and (3) Presenting a modification that, while losing the metric property, allows one to control relative influence of the two groups. This framework is illustrated for registering and clustering shapes of COVID-19 rate curves, identifying essential patterns, minimizing mismatch errors, and reducing variability within clusters compared to previous methods.